User:NOrbeck/Permanent tide

Permanent tide. Mean lunisolar and self gravitation tide. Potential and deformation. Mean sea level. Including the mean solid earth tide.

Introduction

 * Realistic tide-free system
 * Conventional tide-free system
 * Zero tide system
 * Mean tide system

Tidal reference frames
When describing the treatment of the permanent tide in geodetic quantities it become useful to define the various tidal reference frames to which the geodetic quantities refered. The following terminology which is most often used in discussions of the permanent tide


 * Tide free values refer to values which exclude all tide effects
 * Mean tide values refer to values which include both the direct and indirect permanent tide effects
 * Zero tide values refer to values which include the indirect permanent tide effects only and exclude the direct permanent tide effects

EGM96 File description
The file contains fully-normalized, unitless spherical harmonic coefficients for a gravitational model complete from degree 2 order 0, to degree and order 360. These coefficients are consistent with scaling values of GM and a below:


 * $$ V( r, \theta, \lambda ) = \frac{GM}{r}(1+\sum(degree)(a/r)^n \sum( order ) C_{nm}*Y_{nm}( \theta, \lambda )) $$

equal to:
 * $$ GM = 3986004.415E8 \mathrm{ m^3/s^2 }, a=6378136.3 \mathrm{m} $$

The C(2,0) coefficient of this model is in the tide free system. The file contains 65338 records, each record containing:

( n, m, Cnm, Snm, sigmaCnm, sigmaSnm ) --> FORMAT( 2I4, 2E20.12, 2E16.8)

Note that the values concerning the transformation of C(2,0) from the tide-free to the zero tide system, the rates of C(2,0), C(2,1) and S(2,1), and the reference C(2,1) and S(2,1) at epoch Jan 1 1986 are: $$ C20( \text{ zero tide } ) = C20( \text{ tide free } ) - \frac{ 3.11080e{-8} .3 }{ \sqrt(5) } $$

This transformation is documented in NASA's Technical Memorandum 100775 "Consideration of Permanent Tidal Deformation in the Orbit Determination and Data Analysis for the Topex/Poseidon Mission" by Rapp et al., (1991).

Coefficient rates: C20(dot) = 1.16275534e-11  (per year) C21(dot) = -0.32e-11       (per year) S21(dot) = 1.62e-11        (per year) The above rates are held fixed in the solution. No other rates are modeled. The values of C21 and S21 at epoch Jan 1 1986 are held fixed at: C21 = -.1869876359548955E-09  S21 =  .1195280120306540E-08 All values and rates above refer to unitless fully-normalized coefficients.